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Question #43746

Difficulty: 8/10 | 🟢 Free

The Question

A photon of initial energy $E_{\gamma}$ is emitted from a stationary source at the origin $x=0$ at time $t=0$ , traveling along the $+x$ -axis in a vacuum. An observer of mass $m$ and charge $+q$ is initially at rest at $x=L$ . At $t=0$ , a uniform electric field $\vec{E} = E \hat{i}$ is switched on. The photon, being electrically neutral, is unaffected by the electric field. Assuming the observer's velocity remains strictly non-relativistic ( $v \ll c$ ), what is the energy of the photon as measured by the observer at the exact instant the photon intercepts them? (Express the answer to the first order in $v/c$ , where $c$ is the speed of light).

Options

A.
$E_{\gamma} \left( 1 - \frac{qEL}{mc^2} \right)$
B.
$E_{\gamma}$
C.
$E_{\gamma} \left( 1 + \frac{qEL}{mc^2} \right)$
D.
$E_{\gamma} \left( 1 - \frac{qEL}{2mc^2} \right)$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Photon Neutrality|Frame of Reference|Impulse-Momentum Theorem

Why This Question Is Tricky

Common Mistakes

This question tests the conflation of a photon's electrical neutrality with the frame-invariance of its energy.

Students often incorrectly assume that because a photon has zero charge and is unaffected by the electric field in the lab frame, its energy remains $E_{\gamma}$ for all observers in that region (leading to Trap Option B).

They fail to recognize that energy is a frame-dependent component of the four-momentum vector.

The accelerating observer constitutes a non-inertial frame, and the photon's energy must be evaluated using the relativistic Doppler shift based on the observer's instantaneous velocity at the moment of interception.

Option D is another trap where students incorrectly apply the work-energy theorem or average velocity instead of instantaneous velocity.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Dual Nature of Radiation and Matter - Class 12
Concept	Photon Neutrality
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free